Question

compare the y-intercepts and rates of change of the following items.

i: ( y = 1.5x + 3.5 )

ii:

x	y
-2	1.5
-1	2.5
0	3.5
1	4.5
2	5.5

a. the rates of change are the same, but the y-intercepts are different.
b. the items have different y-intercepts and different rates of change.
c. the y-intercepts are the same, but the rates of change are different.
d. the items have the same y-intercepts and the same rate of change.

Explanation:

Step1: Identify I's rate and intercept

For $y = 1.5x + 3.5$, rate of change (slope) $m_1 = 1.5$, y-intercept $b_1 = 3.5$.

Step2: Calculate II's rate of change

Rate $m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2.5 - 1.5}{-1 - (-2)} = 1$.

Step3: Find II's y-intercept

Use $x=0$, $y=3.5$, so $b_2 = 3.5$.

Step4: Compare values

$m_1 = m_2 = 1.5$, $b_1 = b_2 = 3.5$. Both are equal.

Answer:

D. The items have the same y-intercepts and the same rate of change.